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```1 1 22                           Appendix VL

slip without trouble if kept lubricated, indeed both the clutches
Figs. 990 and 991, are intended to be filled with oil under circu-
lation.

Pp. tfj and 8j2. Efficiency of Worm Gear. — Exten-
sive experiments- were made by Messrs. Wm. Sellers & Co. to
determine the efficiencies of worm and spur gear at various
speeds, and the results are set out in Fig. 992. The upper curve
is for simple spur gear, where the shafts are of course parallel, or
enclose an angle of o° ; and the angle w, enclosed by the tooth
line and a normal to the shaft, ^s 90°. Here the efficiencies rise
from 90% to 98% as the pitch-line speed is varied from 3 to 200
ft. per m. The remaining curves shew the efficiencies of worm
gear when designed as in the diagram. Taking the lowest curve
the angle of thread is 5°, and the shaft angle is 85°, causing the
efficiency to vary between 40% and 78%. These figures include
all bearing losses.                                                            *

The frictional resistances in worm gear are caused by (i) the
wheel and worm bearings, (2) the roll of the teeth, (3) the sliding
of the thread, (4) the thrust of the worm. The last two are the
greatest of all, and every effort should be directed towards their
decrease. Mr. C. W. Hill plotted the curves in Fig. 993 from
the theoretical formula :                          ,

vas.
Efficiency

.

«                                                                   27TT

Where       /z = coefficient of friction*

.     p = pitch of teeth or of thread.

r = pitch radius of driver, worm, or wheel.

The left-hand set of curves, are when the worm drives the
wheel, and the right-hand set when the wheel drives the worm :
and each curve is for a different value of /*, The efficiency thus
stated, it must be noted, refers only to the sliding Motion of the
teeth, and all the before-mentioned losses must be included if the
worm gear is to be considered as a- whole. The diagram shews
some interesting facts, however. Thus, the maximum efficiency
is reached when, the thread angle is about 25° to 30% which```